Question

The emissivity of tungsten is approximately 0.35 A tundsten sphere 1 cm in radius is suspended within a large evacuated incloser whose walls are at 300 K. What power input is rquired to maintain the sphere at a temperature of 3000 K? ($\sigma =5.67\times {10}^{-8}inSIunit$ )

• A. 1020 W
• B. 2020 W
• C. 3020 W
• D. 4020 W

Answer 1

The correct option is A 1020 W

Solution :- Power input for temp maintenance = power radiated

power radiated = $\frac{d\theta }{dt}$

By steplan's law,

$\frac{d\theta }{dt}=\left(\epsilon \right)\left(4\pi R^2\right)b{T}^4$

$\frac{d\theta }{dt}=\left(0.35\right)(4\times 3.14\times ({10}^{-2}{)}^2)\times 5.67\times {10}^{-8}\times (3000{)}^4$

$\frac{d\theta }{dt}=2020w$

So, power input = 2020w

Note : Here we are neglecting the

power observed from the surrounding

as the radiated power is quite high

than that

Option - B is correct.